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JEE MAIN - Physics (2025 - 29th January Evening Shift - No. 5)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R) : In isothermal process, PV = constant, while in adiabatic process $PV^{\gamma}$ = constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below:

(A) is true but (R) is false
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
(A) is false but (R) is true
Both (A) and (R) are true and (R) is the correct explanation of (A)

Explanation

We know, ideal gas equation,

$\mathrm{Pv = nRT}$

For isothermal process, T = constant

$\mathrm{\Rightarrow PV = const.}$

$\mathrm{\Rightarrow P \propto \frac{1}{V}}$

For an adiabatic process,

$\mathrm{PV^r=constant}$

JEE Main 2025 (Online) 29th January Evening Shift Physics - Heat and Thermodynamics Question 25 English Explanation

We can see, for the same pressure incresement, $${P_2} - {P_1}$$, $$\left( {{v_4} - {v_3}} \right) > \left( {{v_2} - {v_1}} \right)$$

i.e. the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Hence, option 4 is corret.

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